Abstract For finite strain plasticity, we use the multiplicative decomposition of the deformation gradient to obtain a differential-algebraic system (DAE) in the semi-explicit form and solve it by a half-explicit algorithm. The terminology HERK is synonym of Half-Explicit Runge-Kutta method for DAE. The source is here the right Cauchy-Green tensor and an exact Jacobian of the second Piola-Kirchhoff stress is determined with respect to this source. The system is composed by a smooth nonlinear first-order differential equation and a non-smooth algebraic equation. The development of a half-explicit constitutive integrator is the content of this work. The integration makes use of an explicit Runge-Kutta method for the flow law complemented by the yield constraint. The flow law is a first-order differential equation and the yield constraint (including the loading/unloading conditions) is seen as the invariant of system. A half-explicit method is adopted to ensure satisfaction of the invariant. The resulting scalar equation is solved by the Newton-Raphson method to obtain the plastic multiplier. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Iso-error maps are presented for a combination of Neo-Hookean material using the Hill yield criterion and a associative flow law. Two complete numerical examples are presented.

中文翻译：

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有限应变全各向异性塑性模型的 HERK 积分

摘要 对于有限应变塑性，我们利用变形梯度的乘法分解得到半显式形式的微分代数系统（DAE），并用半显式算法求解。术语 HERK 是 DAE 的半显式 Runge-Kutta 方法的同义词。此处的源是正确的柯西-格林张量，并且关于该源确定了第二 Piola-Kirchhoff 应力的精确雅可比行列式。该系统由一个光滑的非线性一阶微分方程和一个非光滑的代数方程组成。半显式本构积分器的开发是这项工作的内容。积分使用明确的 Runge-Kutta 方法来获得由屈服约束补充的流动定律。流动定律是一阶微分方程，屈服约束（包括加载/卸载条件）被视为系统的不变量。采用半显式方法来保证不变量的满足。得到的标量方程通过 Newton-Raphson 方法求解以获得塑性乘数。我们利用弹性曼德尔应力结构，它与塑性应变率功率一致。使用希尔屈服准则和关联流动定律为 Neo-Hookean 材料的组合呈现等差图。给出了两个完整的数值例子。得到的标量方程通过 Newton-Raphson 方法求解以获得塑性乘数。我们利用弹性曼德尔应力结构，它与塑性应变率功率一致。使用希尔屈服准则和关联流动定律为 Neo-Hookean 材料的组合呈现等差图。给出了两个完整的数值例子。得到的标量方程通过 Newton-Raphson 方法求解以获得塑性乘数。我们利用弹性曼德尔应力结构，它与塑性应变率功率一致。使用希尔屈服准则和关联流动定律为 Neo-Hookean 材料的组合呈现等差图。给出了两个完整的数值例子。